After a week's stay in the hospital for internal injuries suffered during a boogie boarding accident, 13-year-old Christopher Schwarzenegger is improving and is expected to be released by mid-week, a family source tells PEOPLE.

Maria Shriver has kept vigil at her youngest son's bedside since he was admitted to an L.A. hospital with a collapsed lung, broken bones and broken ribs on July 17.

"She was shaken horribly," says a source close to Shriver, who was with Christopher on the Malibu beach when he got caught in a powerful wave.

To all the upheaval in their lives, Maria Shriver and Arnold Schwarzenegger can now add what they call this "very scary week."

"A few days ago our son Christopher suffered an accident at the beach," the estranged couple say in a statement after the 13-year-old boy was hospitalized in serious condition.

Christopher was boogie boarding on Sunday in Malibu, when something went wrong and he suffered a collapsed lung, broken bones and broken ribs, a source tells PEOPLE. His mother was with him on the beach, says the source.